Unbiased Instrumental Variables Estimation under Known First-Stage Sign

Isaiah Andrews and Timothy Armstrong
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Isaiah Andrews: Harvard Society of Fellows

No 1984R5, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution.

Keywords: Weak instruments; Unbiased estimation; Sign restrictions (search for similar items in EconPapers)
JEL-codes: C26 C36 (search for similar items in EconPapers)
Pages: 66 pages
Date: 2015-02, Revised 2016-11
Note: Includes Supplemental appendix
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Published in Quantitative Economics, (July 2017), 8(2): 479ï¿½503

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Related works:
Journal Article: Unbiased instrumental variables estimation under known first‐stage sign (2017)
Working Paper: Unbiased Instrumental Variables Estimation under Known First-Stage Sign (2016)
Working Paper: Unbiased Instrumental Variables Estimation under Known First-Stage Sign (2015)
Working Paper: Unbiased Instrumental Variables Estimation under Known First-Stage Sign (2015)
Working Paper: Unbiased Instrumental Variables Estimation under Known First-Stage Sign (2015)
Working Paper: Unbiased Instrumental Variables Estimation under Known First-Stage Sign (2015)
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